How to add glare/bloom effect to image sequence?
When you move Glare-Treshold from 1 to 0 you can see Glare works (somehow).

Reason why it is not working for red emission object is because you saved sequence as PNG, that is 8-bit color depth, so you lose emission power information.
New scene with the Cube worked, because you composite direct unsaved render - full color depth (high dynamic range), that is not afected by color bit depth of saving file format.
To use image sequence for that purpose you have to set render output as OpenEX (or Multilayered) file format that is 32-bit.

You can alternatively use your rendered 8-bit PNG sequence, but you have only a chance if you:

matte red pixels and increase strengh or
matte red pixels and use glare only on this pass and mix together

One of the possible ways of second option is ...

But as you can see, it will be always difficult to glare red on purple that is similar color. Or you can make it more visible if you dont care it became white glowing object.